50x+x^2/100+200=0

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Solution for 50x+x^2/100+200=0 equation:



50x+x^2/100+200=0
We multiply all the terms by the denominator
x^2+50x*100+200*100=0
We add all the numbers together, and all the variables
x^2+50x*100+20000=0
Wy multiply elements
x^2+5000x+20000=0
a = 1; b = 5000; c = +20000;
Δ = b2-4ac
Δ = 50002-4·1·20000
Δ = 24920000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{24920000}=\sqrt{40000*623}=\sqrt{40000}*\sqrt{623}=200\sqrt{623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-200\sqrt{623}}{2*1}=\frac{-5000-200\sqrt{623}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+200\sqrt{623}}{2*1}=\frac{-5000+200\sqrt{623}}{2} $

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